\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t43\_ordinal6 (TMbLQA6G8yAdrZmyc8mkDiMz39vovGSx7Rz)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ r1\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjded}(X1 \in k2\_ordinal1~X0))\end{array}
\label{hyp:ehhdpfkhggpfchfgggmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_ordinal1~X0)~(k2\_ordinal1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~X0)~(k2\_ordinal1~X0)))))){\unicdbdjdcd}\\
(X1 \in k9\_xtuple\_0~X2)))\end{array}
\label{hyp:ehddedpfpgchegjgogbgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_ordinal1~X0)~(k2\_ordinal1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~X0)~(k2\_ordinal1~X0)))))){\unicdbdjdcd}\\
(\preoh (k4\_ordinal1 \in X0){\unicdcdcdhd}((v2\_ordinal2~X2){\unicdcdcdhd}((v3\_ordinal2~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
((v3\_ordinal1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~X0)){\unicdbdjdcd}(\preoh (X1 \in X3){\unicdcdcdhd}(k4\_ordinal4~\\
X0~X2~X3=X3))))))))\end{array}
\label{hyp:ehcdidpfkhggchfgggmgfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~\\
X0)){\unicdcdcdhd}(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_ordinal1~X0)~(k2\_ordinal1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~\\
X0)~(k2\_ordinal1~X0)))))){\unicdcdcdhd}((v3\_ordinal1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
X0)))){\unicdbdjdcd}(k4\_ordinal4~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfpgchegjgogbgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k2\_ordinal1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
((X2 \in X0){\unicdcdcdhd}(v3\_ordinal1~X2)))\end{array}
\label{hyp:egjdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((r1\_abian~\\
X0~X1){\unicdbdjded}((X0 \in k9\_xtuple\_0~X1){\unicdcdcdhd}(X0=k1\_funct\_1~X1~X0)))\end{array}
\label{hyp:egddpfbgcgjgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}((v1\_ordinal2~X0){\unicdcdcdhd}(v2\_ordinal6~X0))))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_ordinal2~X0){\unicdcdcdhd}((v2\_ordinal2~\\
X0){\unicdcdcdhd}(v3\_ordinal2~X0))))))\end{array}
\label{hyp:dgdgedpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~X0)~(k2\_ordinal1~\\
X0)))){\unicdbdjdcd}(((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_funct\_2~X1~(k2\_ordinal1~X0)~(k2\_ordinal1~\\
X0))){\unicdbdjdcd}((v5\_ordinal1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_ordinal1~\\
X0)~(k2\_ordinal1~X0)){\unicdcdcdhd}(v1\_ordinal2~X1))))))\end{array}
\label{hyp:dgdgbdpfpgchegjgogbgmged}
\end{equation}
\begin{theorem}\label{thm:ehedddpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(v1\_classes2~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k2\_ordinal1~X1)~(k2\_ordinal1~X1)){\unicdcdcdhd}((v2\_ordinal6~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~X1)~(k2\_ordinal1~X1))))))){\unicdbdjdcd}\\
(\preoh (k4\_ordinal1 \in X1){\unicdcdcdhd}((X0 \in X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}\\
(\preoh (X0 \in X3){\unicdcdcdhd}(r1\_abian~X3~X2)))))))\end{array}$$
\end{theorem}
\end{document}
